Abstract
BackgroundTo investigate how patterns of cell differentiation are related to underlying intra- and inter-cellular signalling pathways, we use a stochastic individual-based model to simulate pattern formation when stem cells and their progeny are cultured as a monolayer. We assume that the fate of an individual cell is regulated by the signals it receives from neighbouring cells via either diffusive or juxtacrine signalling. We analyse simulated patterns using two different spatial statistical measures that are suited to planar multicellular systems: pair correlation functions (PCFs) and quadrat histograms (QHs).ResultsWith a diffusive signalling mechanism, pattern size (revealed by PCFs) is determined by both morphogen decay rate and a sensitivity parameter that determines the degree to which morphogen biases differentiation; high sensitivity and slow decay give rise to large-scale patterns. In contrast, with juxtacrine signalling, high sensitivity produces well-defined patterns over shorter lengthscales. QHs are simpler to compute than PCFs and allow us to distinguish between random differentiation at low sensitivities and patterned states generated at higher sensitivities.ConclusionsPCFs and QHs together provide an effective means of characterising emergent patterns of differentiation in planar multicellular aggregates.
Highlights
To investigate how patterns of cell differentiation are related to underlying intra- and inter-cellular signalling pathways, we use a stochastic individual-based model to simulate pattern formation when stem cells and their progeny are cultured as a monolayer
We focus on two candidate mechanisms that may be responsible for pattern formation in populations of stem cells and their progeny, considering patterns which are formed by the transmission of information between cells through either diffusible morphogens or juxtacrine signalling, biasing differentiation pathways
We have shown, using a simple model of diffusive or juxtacrine signalling in a cellular monolayer, how quadrat histograms (QHs) provide a simple measure for distinguishing binary patterns of cellular differentiation from spatially uncorrelated outcomes, and how pair correlation functions (PCFs) may be used to estimate the typical lengthscale of binary patterns
Summary
To investigate how patterns of cell differentiation are related to underlying intra- and inter-cellular signalling pathways, we use a stochastic individual-based model to simulate pattern formation when stem cells and their progeny are cultured as a monolayer. More abstract theoretical models for cellular differentiation are based on the identification of cell fates with distinct attractors of an underlying dynamical system [6]. This idea is embodied in the concept of the ‘epigenetic landscape’ [7], whereby a ball rolling down a slope into a branching network of valleys is analogous to a differentiating cell choosing between distinct fates. Such ideas have been revisited [8,9] in the light of recent observations of differentiating stem cells. Subsequent work has sought to identify explicitly some of the attractors in the dynamical system generated by the cell’s internal regulatory networks [10,11]
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